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On a summer day, you take a road trip through Moses Lake, WA, in a sports car. You start out at a temperature of 21°C in the morning, but the temperature in Moses Lake will reach a peak of 55°C. Each tire on your car holds 15.2 L of nitrogen gas at a starting pressure of 247 kPa. The tires will burst if the internal pressure exceeds 270 kPa.

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ajeigbeibraheem

Here is the complete question.

On a summer day, you take a road trip through Moses Lake, WA, in a sports car. You start out at a temperature of 21°C in the morning, but the temperature in Moses Lake will reach a peak of 55°C. Each tire on your car holds 15.2 L of nitrogen gas at a starting pressure of 247 kPa. The tires will burst if the internal pressure exceeds 270 kPa.

a)  How many moles of nitrogen gas are in each tire?

b) What would the maximum tire pressure be at 50 degrees C?

c) Will the tires burst in Moses Lake? Explain.

Answer:

[tex]n[/tex] [tex]= 1.5384 mole[/tex]

P = 271.9 kPa

Yes, the tires will burst in Moses Lake

Explanation:

Given that

Temperature ([tex]T_i[/tex]) = 21°C = (21 +273)K

= 294 K

Pressure (P) = 247 kPa

Volume (V) = 15.2 L

Numbers of moles (n)= ???(unknown)

Rate constant (R) = 0.082 L. atm/mol. K

a)  How many moles of nitrogen gas are in each tire?

To determine the number of moles of nitrogen in each tire; we use the ideal gas equation:

PV = nRT

re-arranging the equation and making (n) the subject of the formula; we have:

[tex]n= \frac{PV}{RT}[/tex]

[tex]n[/tex] = [tex]\frac{2.44atm*152 L}{0.082L.atm/mol.K*294K}[/tex]

[tex]n[/tex] [tex]= 1.5384 mole[/tex]

∴ the number of moles of nitrogen (n) = 1.5384 moles

b)

b) What would the maximum tire pressure be at 50 degrees C?

at 50°C temperature

Temperature (T) = (50+273)K

= 323 K

where;

V = 1.52 L ;   R = 0.082 L. atm/mol. K and n = 1.54 atm

Still using ideal gas equation:

PV= nRT

[tex]P[/tex] [tex]=\frac{nRT}{V}[/tex]

[tex]P[/tex] [tex]=\frac{1.54atm*0.082L.atm/mol.K*323K}{1.52L}[/tex]

[tex]P[/tex] [tex]= 2.68345 atm[/tex]

Converting the pressure from atm to KPa; we have

[tex]P = (2.6834*101.325)kPa[/tex]

[tex]P=271.9006kPa[/tex]

[tex]P = 271.9 kPa[/tex]

∴ the maximum tire pressure would be 271.9 kPa at 50 degrees C

c) Yes, the tires will have to burst in Moses Lake, because it is stated in the question that if the tire exceeds the internal pressure of 270 kPa, the tires will burst, and here we are with a pressure of 271.9 kPa. As such,  the tire will definitely bursts.

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